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  <section id="module-sympy.geometry.curve">
<span id="curves"></span><h1>Curves<a class="headerlink" href="#module-sympy.geometry.curve" title="Permalink to this headline">¶</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.geometry.curve.</span></span><span class="sig-name descname"><span class="pre">Curve</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">function</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">limits</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L19-L419"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve" title="Permalink to this definition">¶</a></dt>
<dd><p>A curve in space.</p>
<p>A curve is defined by parametric functions for the coordinates, a
parameter and the lower and upper bounds for the parameter value.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>function</strong> : list of functions</p>
<p><strong>limits</strong> : 3-tuple</p>
<blockquote>
<div><p>Function parameter and lower and upper bounds.</p>
</div></blockquote>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong></p>
<blockquote>
<div><p>When <span class="math notranslate nohighlight">\(functions\)</span> are specified incorrectly.
When <span class="math notranslate nohighlight">\(limits\)</span> are specified incorrectly.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">sin</span><span class="p">,</span> <span class="n">cos</span><span class="p">,</span> <span class="n">interpolate</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span><span class="p">,</span> <span class="n">a</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">((</span><span class="n">sin</span><span class="p">(</span><span class="n">t</span><span class="p">),</span> <span class="n">cos</span><span class="p">(</span><span class="n">t</span><span class="p">)),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">functions</span>
<span class="go">(sin(t), cos(t))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">limits</span>
<span class="go">(t, 0, 2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">parameter</span>
<span class="go">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">interpolate</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">16</span><span class="p">],</span> <span class="n">t</span><span class="p">)),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">));</span> <span class="n">C</span>
<span class="go">Curve((t, t**2), (t, 0, 1))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">subs</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">4</span><span class="p">)</span>
<span class="go">Point2D(4, 16)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">arbitrary_point</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">Point2D(a, a**2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="../core.html#sympy.core.function.Function" title="sympy.core.function.Function"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.core.function.Function</span></code></a>, <a class="reference internal" href="../polys/reference.html#sympy.polys.polyfuncs.interpolate" title="sympy.polys.polyfuncs.interpolate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.polys.polyfuncs.interpolate</span></code></a></p>
</div>
<p class="rubric">Attributes</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 47%" />
<col style="width: 53%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p>functions</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>parameter</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>limits</p></td>
<td></td>
</tr>
</tbody>
</table>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.ambient_dimension">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">ambient_dimension</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.ambient_dimension" title="Permalink to this definition">¶</a></dt>
<dd><p>The dimension of the curve.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>int :</p>
<blockquote>
<div><p>the dimension of curve.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">ambient_dimension</span>
<span class="go">2</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.arbitrary_point">
<span class="sig-name descname"><span class="pre">arbitrary_point</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">parameter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'t'</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L92-L146"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve.arbitrary_point" title="Permalink to this definition">¶</a></dt>
<dd><p>A parameterized point on the curve.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>parameter</strong> : str or Symbol, optional</p>
<blockquote>
<div><p>Default value is ‘t’.
The Curve’s parameter is selected with None or self.parameter
otherwise the provided symbol is used.</p>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Point :</p>
<blockquote>
<div><p>Returns a point in parametric form.</p>
</div></blockquote>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError</strong></p>
<blockquote>
<div><p>When <span class="math notranslate nohighlight">\(parameter\)</span> already appears in the functions.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Symbol</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">s</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">([</span><span class="mi">2</span><span class="o">*</span><span class="n">s</span><span class="p">,</span> <span class="n">s</span><span class="o">**</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">arbitrary_point</span><span class="p">()</span>
<span class="go">Point2D(2*t, t**2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">arbitrary_point</span><span class="p">(</span><span class="n">C</span><span class="o">.</span><span class="n">parameter</span><span class="p">)</span>
<span class="go">Point2D(2*s, s**2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">arbitrary_point</span><span class="p">(</span><span class="kc">None</span><span class="p">)</span>
<span class="go">Point2D(2*s, s**2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">arbitrary_point</span><span class="p">(</span><span class="n">Symbol</span><span class="p">(</span><span class="s1">&#39;a&#39;</span><span class="p">))</span>
<span class="go">Point2D(2*a, a**2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="points.html#sympy.geometry.point.Point" title="sympy.geometry.point.Point"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.free_symbols">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">free_symbols</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.free_symbols" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a set of symbols other than the bound symbols used to
parametrically define the Curve.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>set :</p>
<blockquote>
<div><p>Set of all non-parameterized symbols.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span><span class="p">,</span> <span class="n">a</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">free_symbols</span>
<span class="go">set()</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">free_symbols</span>
<span class="go">{a}</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.functions">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">functions</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.functions" title="Permalink to this definition">¶</a></dt>
<dd><p>The functions specifying the curve.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>functions :</p>
<blockquote>
<div><p>list of parameterized coordinate functions.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">functions</span>
<span class="go">(t, t**2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.curve.Curve.parameter" title="sympy.geometry.curve.Curve.parameter"><code class="xref py py-obj docutils literal notranslate"><span class="pre">parameter</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.length">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">length</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.length" title="Permalink to this definition">¶</a></dt>
<dd><p>The curve length.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry.curve</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="p">),</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">length</span>
<span class="go">sqrt(2)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.limits">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">limits</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.limits" title="Permalink to this definition">¶</a></dt>
<dd><p>The limits for the curve.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p><strong>limits</strong> : tuple</p>
<blockquote>
<div><p>Contains parameter and lower and upper limits.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">([</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">3</span><span class="p">],</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="o">-</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">limits</span>
<span class="go">(t, -2, 2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.curve.Curve.plot_interval" title="sympy.geometry.curve.Curve.plot_interval"><code class="xref py py-obj docutils literal notranslate"><span class="pre">plot_interval</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.parameter">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">parameter</span></span><a class="headerlink" href="#sympy.geometry.curve.Curve.parameter" title="Permalink to this definition">¶</a></dt>
<dd><p>The curve function variable.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Symbol :</p>
<blockquote>
<div><p>returns a bound symbol.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">t</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span> <span class="o">=</span> <span class="n">Curve</span><span class="p">([</span><span class="n">t</span><span class="p">,</span> <span class="n">t</span><span class="o">**</span><span class="mi">2</span><span class="p">],</span> <span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">C</span><span class="o">.</span><span class="n">parameter</span>
<span class="go">t</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.curve.Curve.functions" title="sympy.geometry.curve.Curve.functions"><code class="xref py py-obj docutils literal notranslate"><span class="pre">functions</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.plot_interval">
<span class="sig-name descname"><span class="pre">plot_interval</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">parameter</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'t'</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L296-L330"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve.plot_interval" title="Permalink to this definition">¶</a></dt>
<dd><p>The plot interval for the default geometric plot of the curve.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>parameter</strong> : str or Symbol, optional</p>
<blockquote>
<div><p>Default value is ‘t’;
otherwise the provided symbol is used.</p>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>List :</p>
<blockquote>
<div><dl class="simple">
<dt>the plot interval as below:</dt><dd><p>[parameter, lower_bound, upper_bound]</p>
</dd>
</dl>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Curve</span><span class="p">,</span> <span class="n">sin</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span><span class="p">,</span> <span class="n">s</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)),</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">plot_interval</span><span class="p">()</span>
<span class="go">[t, 1, 2]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">)),</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span><span class="o">.</span><span class="n">plot_interval</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
<span class="go">[s, 1, 2]</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="#sympy.geometry.curve.Curve.limits" title="sympy.geometry.curve.Curve.limits"><code class="xref py py-obj docutils literal notranslate"><span class="pre">limits</span></code></a></dt><dd><p>Returns limits of the parameter interval</p>
</dd>
</dl>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.rotate">
<span class="sig-name descname"><span class="pre">rotate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">angle</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L332-L374"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve.rotate" title="Permalink to this definition">¶</a></dt>
<dd><p>This function is used to rotate a curve along given point <code class="docutils literal notranslate"><span class="pre">pt</span></code> at given angle(in radian).</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>angle :</strong></p>
<blockquote>
<div><p>the angle at which the curve will be rotated(in radian) in counterclockwise direction.
default value of angle is 0.</p>
</div></blockquote>
<p><strong>pt</strong> : Point</p>
<blockquote>
<div><p>the point along which the curve will be rotated.
If no point given, the curve will be rotated around origin.</p>
</div></blockquote>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Curve :</p>
<blockquote>
<div><p>returns a curve rotated at given angle along given point.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry.curve</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">pi</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">),</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Curve((-x, x), (x, 0, 1))</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.scale">
<span class="sig-name descname"><span class="pre">scale</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L376-L398"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve.scale" title="Permalink to this definition">¶</a></dt>
<dd><p>Override GeometryEntity.scale since Curve is not made up of Points.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Curve :</p>
<blockquote>
<div><p>returns scaled curve.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry.curve</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">),</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Curve((2*x, x), (x, 0, 1))</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.curve.Curve.translate">
<span class="sig-name descname"><span class="pre">translate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/curve.py#L400-L419"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.curve.Curve.translate" title="Permalink to this definition">¶</a></dt>
<dd><p>Translate the Curve by (x, y).</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Curve :</p>
<blockquote>
<div><p>returns a translated curve.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry.curve</span> <span class="kn">import</span> <span class="n">Curve</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Curve</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">),</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Curve((x + 1, x + 2), (x, 0, 1))</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

</section>


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